洛伦兹平坦空间L-4中的一般弹性曲线

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基金项目: 国家自然科学基金资助项目(10671066);上海市重点学科资助项目(B407)

Generalized Elastic Curves in Lorentz Flat Space L⁴

Department of Mathematics, East China Normal University, Shanghai 200241, P. R. China

摘要: 研究了4维Lorentz-Minkowski空间中，非类光曲线的曲率能量作用的极值曲线．求出了一般弹性曲线的运动方程和3个沿着一般弹性曲线的Killing场，用这些Killing场建立了一个柱面坐标系并用积分表示了一般弹性曲线．
- 一般弹性曲线 /
- 几何粒子模型 /
- Killing场 /
- Lorentz-Minkowski空间
Abstract: The extremals of curvature energy actions on non-null curves in 4-dimensional Lorentz-Minkowski space are studied.The motion equations were worked out and three Killing fields along the generalized elastic curves were found.A cylindric coordinate system by using these Killing fields was constructed and the generalized elastic curves by quadratures were expressed.
- generalized elastic curve /
- geometrical particle model /
- Killing field /
- Lorentz-Minkowskispace

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